how many ways can you roll a pair of 6-sided dice and get an absolute difference less or equal to 8

Question

 nothing

Answer 1

Each die has numbers 1-6 (that is, 6-sided).  There are 36 possible outcomes.  Let's make an "absolute difference" table (much like an addition table).

 

 

First Die                          Second die

                      1       2       3       4       5       6

   1                 0       1       2       3       4       5

   2                 1       0       1       2       3       4

   3                 2       1       0       1       2       3

   4                 3       2       1       0       1       2

   5                 4       3       2       1       0       1

   6                 5       4       3       2       1       0

 

Hmm, it seems that all 36 absolute differences are less than or equal to 8.

 

We could have determined that by simply taking the largest value (6) and the smallest value (1) and determined that the biggest difference that we could ever get was 5.